Coensgen, F.H.

Cummins, W.F.

Molvik, A.W.

Nexsen, W.E. Jr.

Simonen, T.C.

Stallard, B.W.

Coensgen, F. H.

Cummins, W. F.

Molvik, A. W.

Nexsen, W. E., Jr.

Simonen, T. C.

Stallard, B. W.

UNT Digital Library

V This is a prepr int of a paper intended for publication in a journal or proceedings. Since change* may be made before publication, th is prepr in t i s made available with the understanding that it will not be cited or reproduced without the permiss ion of the author. & i, A / UCRL - 7S511 PREPRINT 'lottos' - -w LAWRENCE LIVERMORE LABORATORY University ol Calilomia/Livermore. California PLASMA CONTAINMENT IN 2XII F. H. Coensgen W. F. Cummins A. W. Molvik W. E. Nexsen, J r . T. C. Simonen B. W. S ta l l a rd September 25, 1974 Th,s : i : | . , ; r l M i- --itp ..... ,. ,„ , - l M J spoiiiun-d hi t u- i mi -. . (., Ihe l.'niled Sen fommission. in •i nut X : jft.. ( i;.c z* - s„h makes ani wjrr n l i . w I >CT1[-Il - .1 , r Isjial l i jni l i ty ,i I - • [•" ' ^it-i ' i! pmJuLi ur pi i . t CSS [| . • i . i ' . | . . . r.- f. — i - r i t -t r p u u a r i l , ! This paper was prepared for submittal to Proceedings 5th Conference on Plasma Physics and Controlled Nuclear Fusion </ •_i . . ' i H '-> i\ IAEA-CN-33/D2-1 PLASMA CONTAINMENT IN 2X1I* F. H. Coensgen, W. F. Cummins, A. W. Molvik, W. E. Nexsen, J r . , T. C. Simonen, and B. W. Stallard Lawrence Livermore Laboratory, University of California Livermore, California 94550 ABSTRACT Experiments in the 2XII magnetic mirror device have achieved high beta (6 = 0.3 to 0.5) plasma confinement. Near classical confinement was observed in the range 2 to 5 * 1 0 ^ cm"^ with average ion energies of 1 to 3 keV. The measured electron energy, 50 to 150 eV, was consistent with classical energy transfer from the hot ions. At lower plasma densities, the loss rate departs from classical confinement owing to quasi-classical scattering and ion cyclotron fluctuations. The injection of a 10-A, 20-keV neutral atom beam produced no beam-drivsn instabilities, nor did it increase charge exchange losses. INTRODUCTION f This report discusses results from the 2XII mirror confinement experi-ment[l-4]. In contrast to the 2X device[5], 2XII has minimum B trapping gates, higher mirror ratio, deeper radial well, and magnetic field lines diverted to 3-m-long end tanks rather than terminated on nearby vacuum chamber walls. These improvements in magnetic field geometry yielded consistent and more reproducible operation, permitting extensive plasma diagnostics and studies of plasma confinement. The principal results of the 2XII experiment include: * This work was performed under the auspices of the U.S. Atomic Energy Commission. 2 • Achievement of plasma confinement a t $ a 0.4, the l imit of plasma equilibrium in 2X1I. • Demonstration of near -c lass ica l confinement of 1- t o 3-IceV plasmas a t high densi t ies (wj* > to§ e). • Indirect evidence of enhanced sca t t e r ing due to high-frequency convective waves at lower plasma d e n s i t i e s . • Measurement of electron temperatures indica t ing confinement of e lectron energy in open-ended geometry. • Ident i f ica t ion of an ion cyclotron i n s t a b i l i t y tha t i s l imited to low amplitudes and s t ab i l i zed by ex te r io r plasma in a nonquiescent operating mode. o Injection of a I0-A, 20-keV neutral beam. HIGH BETA CONFINEMENT Measurements of mean ion energy and peak density indicate that plasma betas[3] were as high as the theore t i ca l maximum[6]. Ion energy was determined from charge exchange measurements and density from the at tenuat ion of a 16-keV hydrogen atom beam, which were cross-checked by Thomson sca t te r ing and, at lower dens i t i e s , by microwave interferometry. Central plasma energy density (nE) vs magnetic f ie ld energy (B^) i s p lo t ted in Fig. 1 for the high energy-density shots with magnetic guide f ie lds of 0 .5 , 1.0, and 2.0 kG. We conclude that the i n i t i a l beta was high, 0,3 to 0 .5 , and the i n i t i a l energy density was h: Her for higher guide f i e l d s . This l a t t e r conclusion indicates that at lower f i e l d s , the plasma was beta Umited, ra ther than limited by plasma in jec tor output. For a l l cases in Fig. 1, the r a t i o of maximum measured to maximum theore t i ca l betas for mirror equilibrium (B c) was 0.9 ± 0 . 1 . The theore t ica l beta l imit increases with the mirror r a t i o [ 6 ] . In 2XII the mirror r a t i o decreases from 3:1 with the trapping gates to 2:1 with the compression f i e ld . Plasma density has been observed to decrease with the mirror r a t i o to maintain 3=6 C. Thus the magnitude and time depend­ence of the maximum observed beta indicate that hot-ion plasmas can be confined at high values of be ta , limited only by mirror equilibrium. PLASMA CONFINEMENT IN 2X11 Experiments in 2XII have indicated that high-density {inie > wj: e), quiescent plasmas with 1- to 3-keV ion energies can be produced with losses close to the Coulomb r a t e . At lower dens i t i e s , more rapid losses are measured in agreement with calcula t ions based on quas i -c lass ica l s ca t t e r i ng . In a second operating mode, when plasma i s injected l a t e r e l a t i ve to the trapping magnets, ion cyclotron f luctuat ions and enhanced plasma losses are measured. Fluctuations in th i s non-quiescent mode are eliminated, while maintaining high ion energies (2 to 3 keV), by discontinuing ge t te r ing in the central vacuum chamber. The quiescent mode of 2X11 has been studied extensively. As the density decays in time during a given shot , the density dependence on nx at high densi t ies [ i . e . , ( w p e / u c e ) 2 > 1] appears to agree with tha t calculated by Baldwin and Callen[7] for plasma loi^es a r i s ing from quas i -c lass ica l sca t t e r ing : J A cxp-ji- ds In[yF(y)) ( n / S ' i ' / " . , \ <->. ^(?)" ! (--y ! / - ' where e = (w /ti 1-5 n/B*" e i>o cc if n is in units of 1 0 1 3 cm"J and B is in tcsla. The exponential is independent of density if e e » 1. Hence, in the higher density range, if Tj, T c, and the ion velocity function all remain constant as the plasma density decreases, the last term of the above expression is simply a product of a constant and a function of n/B2. For these conditions, the graph of 1/nT vs (n/B-) - 1/-(1+n/B2)"3''2 should be a straight line with an intercept equal to l/(nT)€, where (ni) c is the value calculated for Coulonb scattering. The slope of the line is proportional to the convective amplification of the fluctuation spectrum. Data from two relatively low-energy quiescent runs arc shown in Fig. 2. A straight line can be drawn through the high-density data for each run. The values of (nx) c derived from the intercepts of these two lines are a factor two less than those calculated using a two-dimensional Fokkcr-Planck code[8], Within the accuracy of the data, ( n T ) c values derived from the intercepts increase as T 3'^, in agreement with Coulomb scattering. The fact that the slope of the B-C curve for the 2.7-keV run is aboi'.t six tines greater than that of the 1.3-keV run (Fig. 2) is not in agreement with the behavior expected from the 1/aj factor in the exponent of liq. (1). However, the convective growth rate is a function of the shape of the ion energy distribu­tion. Measurements over a number of shots indicate no systematic dependence of the slope on aj. In the second mode of operation, the plasma exhibits ion cyclotron fluctuations. These fluctuations (0.02 < o'ucj < 4) are detected by microwave scattering and by high-impedance electrostatic probes measuring potential fluctuation amplitude, $. The measured frequency spectrum initially centers near d)cj; but as the instability develops, the frequency spectrum broadens and decreases below w cj. Azimuthal wavelength measurements indicate that kyaj - 4 and that the wave uhase velocity is about one-fourth the ncw-.i ion thermal speed in the ion t1 lagnetic drift direction. Probes separated by 10 cm along a given field .ne are in phase, indicating that k 2a, < 0.3. These fluctuations thus exhibit characteristics of Drift-Cone instability[9]. In quiescent cases ($ « T e ) , the ion cyclotron fluctuations do not limit confinement. In less quiescent cases (4> - T e ) , they produce enhanced plasma losses and stochastic acceleration of ions to high energy. The fluctuations were suppressed by discontinuing gcttering of the central high-vacuum chamber. Such partially gettered operation increase' the exterior plasma density from about 1/2% to 5?» of the center density. It also increased the centei density and containment time so that nT increased by a factor of two to three, to the range 2 » 10 1 0 cm - 3 s. 1_ dn 2 dt 1_ nt 4 liUiCTRON I.NI.PCY t . i ' M T . ! ' n ' . ; Thomson-sca t t e r ; ] . ; : ncasu rc i i en t s of e l e c t r o n t e n p e r a t u r e [ I O ] , t o g e t h e r wi th i o n - e n e r g y and d e n s i t y n e a s u y e n e n l s , p r o v i d e a b a s i s fo r c x a n i n i n g ene rgy t r a n s p o r t fro'- hot deut>-ri<i~ ions t o t h e c o o l e r e l e c t r o n s : dh / d t :>.: * 1'.-"J * >. I n . * . 1 n IV. IV ' x ' : - 4/T kcV/s . (2) c e l e * J E l e c t r o n arid ton e n e r g i e s >.'-.,. ;«:.! l> j) ,n well as p l a s m p o t e n t i a l (4) a r e in keV, d e n s i t y i s n. >-: , .,.',,. e;e.- tn>» ) : ; i t i n e CO in s . The d e n s i t y decay of F ig . 3a [ t i r c l i 1 - i.;n o b t a i n e d t'nm Thor.son s c a t t e r i n g and nicrowavc i n t e r -f e r o n c t r y . lhe rx .i^i.rcd n-ai, ton ene -gy, shown as t h e no i sy curve in Fie.. Sb, was o b t a i n e d :y c e n p u t e r r e d u c t i o n of the l i - c h a n n e l , charge exchange d e t e c t o r [ 1 1 ] . The e l e c t r o n t e r p e r a v u r e neasureraents i n F i g . 3c ( c i r c l e s ) were o b t a i n e d t'ror. .e- .eral p l a s m sho t s with t h e l a s e r (J-swi t ched at. d i f f e r e n t t i n e s . In each shot . the dciisit ; , decay and ncan ion energy vs t i r e was checked for r ep ruduc : ! : 11 : > ::.•.• v a l i d i t y of Fq. ( - ) was c o n f i r n e d by t a k i n g t h e Fokker-Plane* : : . : : : • . a:.d :ov. energy to c a l e u l a i e t h e ncan e l e c t r o n energy us ing I . i . _ :':.i u-rcencnT wi th the Fol.lcr-Fl.jncS, c a l c u l a t i o n i s i n d i c a t e d bv the c . . - i l . r : ; :.r c r o s s e s wi t ! t h e d o ; t e d l i n e i n F i g . ->c. S i n i l a r l y , c a l c u l a t i i:i; the r ea r e l e c t r o n eiierp.y fo r t h e e x p e r i m e n t a l obse rved d e n s i t y and IOI. c:;cr • •..:- e - t . ' s n the s o l i d l i n e , which is w i t h i n 30* of t h e measured e l e c t r o n ra r n .e .-oncliidc t h a t for t h i s c a s e , e l e c t r o n end l o s s e s c o n s t i t u t e the i r ; : - . i ! . ' . e l e c t ie;'. energy loss p r o c e s s . \ u rn< .u hi A'' r •; r : : •. ; •.; • -:••: -.; he have ; j ; ; e L : e e 1 • ' r f e i t h e r hydrogen or d e u t e r i u n 20-kcV n e u t r a l ?.toffls[irj i r . ' i ' 'X: ' -.-- t: t e s •' Pear, a t t e n u a t i o n , d e l i v e r i n g lo •' of energy t o the p_lasr.a. • ;• c - . p a r i s e a , , the energy con ten t of a 2-keV 2X11 p l a s n a a t 2 * l o ' J cn':' i s 'ij ' . !'i e s t i r a t i n g t h e energy d e l i v e r e d by t h e i n j e c t e d p a r t i c l e s , we m c h . J i ;:e.-.:i!.i: hv t h e r i s i n ; : r ,a ; :net ic f i e l d of p a r t i c l e s t r apped du r ing nagne ' . i c c o n p r e s s i o n . S ince t h e lumber of bean p a r t i c l e s t r a p p e d by the p l a s n a i s only a few .percent of t h e p l a s n a d e n s i t y , however, n e a s u r e n e n t s wi th and wi thout n e u t r a l bean i n j e c t i o n show o n l \ s n a i l d i f f e r e n c e s and i n d i c i t e t ha t the bean does not s i g n i f i c a n t l y change HT. Thi e f f e c t of bea r i n f e c t i o n on e l e c t r o n t e n p e r a t u r e i s e s t i n a t c d t o be 104. A s n a i l e l e c t r o n l o - p e r a t u n - i n c r e a s e , wi t l i in the u n c e r t a i n t y in t h e Thonson-s c a t t e r i n g measure - . ! . * , is observed . Forward-.in,; 1 . : : r • .erew.ivt- s c a t t e r i n g and e l e c t r o s t a t i c p robe n c a s -u r e n c n t s show i.e. s :;;-i::'i - a:.t n o i s e i n c r e a s e in the f requency range 0 . 2 < u /u i C j < 3 wi th n e u t r a l : ear in ; c c t tor.. '.e enhanced s t o c h a s t i c ion a c c e l e r a t i o n was obse rved . ii.es.- .i. i e c l i or. e x p o r i n e n t s thus i n d i c a t e d t h a t wh i l e low bean c u r r e n t s produce no hen;.- dr i vol. i n s t a b i l i t i e s nor enhanced cha rge exchange l o s s e s , h i r h e r c u r r e n t s a re n e c e s s a r y t o s u s t a i n t h e 2X11 p l a s n a . 2X1 III In o r d e r t o c a p i t a l i : e on the f i u o r a b l e h i g h - d e n s i t y r e s u l t s of 2X1! a new nagnet s y s t e n (2X1 111! has been b u i l t . The fundnnenta l changes in 2X11D (see Table 1) a re i t s l a r g e r t r a n s v e r s e vacuum chanber s i r e and i t s f i v e -t i m e s - l a r g e r a c c e s s a r e a p e r i l t t ine , t h e i n j e c t i o n of 600 A of 20-keV hydrogen a t o n s . A n e u t r a l hoa:\ i n i e c t i o n s y s t e r c o n s i s t i n g of twe lve 20-kcV, 5 50-A modules[13] is being placed into operation to increase nr. The injection system is capable of increasing the mean ion energy above 10 keV by injecting particles over a wide energy spread with sufficient intensity to maintain a high density, beta-limited plasma. REFERENCES (I] COFNSGEN, F. II., et al, 5th European Conf. Contr. Fusion Plasma Phys. (Proc. Conf. EURATOM-CEA Grenoble, 1372) 2_, 71. [2] COENSGEN, F. I!., ct al., 6th F.uropean Conf. Contr. Fusion Plasma Phys. (I'roc. Conf. Moscow, 1973). [3] MOLVIK, A. K., ct al., Phys. Rev. Lett. 32 (1974) 1107. [4] SIMO.vcv, T. C, ct al., Nucl. Fusion 14 (1974) 61. [5] COENSGEN, F. II., ct al., 4th Int. ConfT Plasma Phys. Contr. NucL. Fusion !(cs. (I'roc. Conf. Madison, 1971) 2_, IAEA (1971) 721. [6] HALL, L. S., Phys. Fluids |S_ (1972) 882. [7] BALDWIN, I). E., CALLEN, J. D., Phys. Rev. Lett. 28 (1972) 1686. [8] PUTCII, A. H., .Ir., et al.. Plasma Phys. 1£ (19727~211. [9] BALDKI.V, D. E., et al., 4th Int. Conf. Plasma Phys. Contr. .Vucl. Fusion Res. (Proc. Conf. Madison, 1971) 2_, IAEA (1971) 73S. [10] SI MOSES, T. C , et al., Bull. Am. Phys. Soc. ]£ (1973) 1320 and to be published. [II] NEXSEN, K. I:., JR., tt al.. Bull. Am. Phys, Soc. 17. (1972) 98S and 1£ (1971) 1240. [12] EHLF.RS, K. If., et al., 2nd Int. Conf. Ion Sources (Proc. Conf. Vienna, 1972), 1_ 259 and 264. [13] PYLE, R. V., ct al., Paper 1)2 "\ these Proc. Table I. Magnetic field characteristics of 2XII arid 2XIIB. Parameters 2XII 2XIIB Maximum d.c. guide field (kG) Maximum central field (kG) Magnetic field rise time (nis) Magnetic field decay time (ms) Longitudinal mirror ratio Distance between mirrors (cm) Radial well depth at wall {%) Maximum plasma diameter (cm) Transverse access at coil (m^) 2 3 6 . 5 9 0 .4 0 8 10 2 2 115 150 21 64 30 100 0.". 1 Figure Captions Fig. 1. Plasma pressure nE vs magnetic pressure b for magnetic guide fields. Constant beta lines are shown. Fig. 2. Comparison of 2XII data with the Baldwin-Callen scaling law. Fig. 3. Electron density, ion energy, and electron energy vs time for a quiescently decaying plasma. 15h a> l l l h -10, ... ! / ( 2 . B - ° - 5 % / (1.0 kG)^ / ?// 1 3 kG)-v ^ _ f/ .-• /Xf - / . / / o V ^ M 0 . 5 kG) i 10 B 2 (kG) 15 1.4 1.2 1.0 0.8 0.6 0.4 0.2 " i — i — i — | — I — I — r • E = 2.7 keV 1 ' ' I ' ' ' lo o o . (nx) = 1 * 1010cm"3s From intercept0 o 1.3 keV . , (m) = 2.8 x 10s cm"Js From intercept _ J I I I I l_ J_ 0 0.2 0.4 0.6 0. (n/B 2)" 1 / 2 (1 + n/B 2)" 3 / 2 J_LJ I . I L_ 4.2 0.85 0.42 (nX10"13 cm"3) J_d I 1 L 10 3 2 1.5 1 u e> 0.21 0.5 K QI ' 1 1 1 1 I L gl I I I I I I 1 I 0.2 0.4 0.6 0.8 1.0 Time (ms) Experimental measurements Fokker-Planck calculation + + + Electron energy calculated by Eq. (2) for Fokker-Planck density and ion energy time dependence Electron energy calculated by Eq. (2) for experimentally measured density and ion energy time dependence 

Plasma containment in 2XII

Plasma containment in 2XII

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